Method and system for proactive heating-based crack prevention in 3D printing

ABSTRACT

A computer program product for proactive heating-based crack preventing in three-dimensional printing is provided. The computer program product includes a computer readable storage medium having program instructions embodied therewith. The program instructions are readable and executable by a processing circuit to cause the processing circuit to read a three-dimensional model to be printed, determine if the read three-dimensional model has open-ended or closed-ended layers, for each closed-ended layer, calculate start and end heating times and amount of heat requirement for materials of the closed-end layers and control a heating of the closed-ended layers in accordance with the calculation during a laying down of each of the closed-ended layers.

BACKGROUND

The present invention relates to three-dimensional printing or additivemanufacturing and, more specifically, to a method and system ofproactive heating-based crack prevention in three-dimensional (3D)printing or additive manufacturing.

Three-dimensional printing involves successive layers of material beinglaid down onto a substrate or each other from a dispensing head that iscontrolled by a computer. Three-dimensional printed objects can be ofalmost any shape or geometry and are derived from a three-dimensionalmodel or other electronic data source that is loaded into thecontrolling computer. The dispensing head is a component of athree-dimensional printer, which itself is a type of industrial robot.

In the case of large three-dimensional printed objects, completion ofthe laying down of each successive layer requires a relatively longperiod of time as the dispensing head traverses the length of the layer.This leads to the generation of a time gap between the laying down ofthe starting point of a layer to an end point of the laying down of thelayer. Thus, by the time the dispensing head reaches the end point, thematerial dispensed at the start point may harden and may lead to a finegap between the starting and end point of the layer.

SUMMARY

According to an embodiment of the present invention, a computer programproduct for proactive heating-based crack preventing inthree-dimensional printing is provided. The computer program productincludes a computer readable storage medium having program instructionsembodied therewith. The program instructions are readable and executableby a processing circuit to cause the processing circuit to read athree-dimensional model to be printed, determine if the readthree-dimensional model has open-ended or closed-ended layers, for eachclosed-ended layer, calculate start and end heating times and amount ofheat requirement for materials of the closed-end layers and control aheating of the closed-ended layers in accordance with the calculationduring a laying down of each of the closed-ended layers.

According to another embodiment of the present invention, a computingsystem for proactive heating-based crack preventing in three-dimensionalprinting is provided. The computing system includes a computer readablestorage medium having instructions stored thereon that are executable bya processing circuit to cause the processing circuit to read athree-dimensional model to be printed, determine if the readthree-dimensional model has open-ended or closed-ended layers, for eachclosed-ended layer, calculate start and end heating times and amount ofheat requirement for materials of the closed-end layers and control aheating of the closed-ended layers in accordance with the calculationduring a laying down of each of the closed-ended layers.

According to yet another embodiment of the present invention, acomputer-implemented method for proactive heating-based crack preventingin three-dimensional printing is provided and includes reading athree-dimensional model to be printed, determining if the readthree-dimensional model has open-ended or closed-ended layers, for eachclosed-ended layer, calculating start and end heating times and amountof heat requirement for materials of the closed-end layers andcontrolling a heating of the closed-ended layers in accordance with thecalculation during a laying down of each of the closed-ended layers.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The forgoing and other features, and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 is a schematic illustration of a computing system;

FIG. 2 is a schematic diagram of a three-dimensional printer;

FIG. 3 is a top down view of a laying down of an open-endedthree-dimensionally printed layer;

FIG. 4 is a top down view of a laying down of a closed-endedthree-dimensionally printed layer;

FIG. 5 is an axial view of wall portions provided to containthree-dimensional printing material in liquid form in accordance withembodiments;

FIG. 6 is a schematic diagram of a computer program product forproactive heating-based crack prevention in three-dimensional printing;

FIG. 7 is a flow diagram illustrating a deployment process of thecomputer program product of FIG. 6; and

FIG. 8 is a flow diagram illustrating a computer-implemented method forproactive heating-based crack prevention in three-dimensional printing.

DETAILED DESCRIPTION

As will be described below, a method and system are provided forcontrolling a three-dimensional printing of an object by heatingclosed-ended layers to facilitate crack prevention in those closed-endedlayers. Such heating will allow start and end points of closed-endedlayers to be maintained in a liquid state during the time period takento lay down the layer so that subsequent crystal formation will besubstantially uniform along an entire length of the closed-ended layerand perfect (or nearly perfect) joining can be achieved. The heatingwill be controlled by heating a controller in accordance with heatingalgorithms stored therein and various layer material properties andcrystal formation temperatures.

With reference to FIG. 1, a computing system 10 is provided and may beconfigured for example as an enterprise computing system or as apersonal computing system. In either case, the first computing system 10includes first, second and third computing devices 11, 12 and 13 andservers 15 which are configured to be networked together forcommunication purposes. Each of the first, second and third computingdevices 11, 12 and 13 and the servers 15 may include among otherfeatures a processing circuit 20, a display, user input devices and anetworking unit as well as a computer program product 100 for proactiveheating-based crack prevention in three-dimensional printing.

The processing circuit 20 may be provided as a micro-processor, acentral processing unit (CPU) or any other suitable processing device.The display may be provided as a monitor and is configured to displaydata and information as well as a graphical user interface to anadministrator or user. The user input devices may be provided as a mouseand a keyboard combination and are configured to allow the administratoror user to input commands to the processing circuit 20. The networkingunit may be provided as an Ethernet or other suitable networking deviceby which the first, second and third computing devices 11, 12 and 13 andservers 15 are communicative.

With reference to FIG. 2, any one or more of the first, second and thirdcomputing devices 11, 12 and 13 and the servers 15 may be coupled to athree-dimensional printer 16. For purposes of clarity and brevity,however, the following description will relate to the exemplary case inwhich the first computing device 11 is coupled to the three-dimensionalprinter 16.

As shown in FIG. 2, the three-dimensional printer 16 includes a housing160, a dispenser 161, servo elements 162 that are supportively andmovably disposed in the housing 160 to control a movement of thedispenser 161 and a heating element 163. The housing 160 is formed todefine an empty space in an interior thereof and the dispenser 161 isconfigured to dispense three-dimensional printing materials onto asubstrate within the empty space in order to additively manufacture agiven object. This object is formed in accordance with athree-dimensional model, which may be loaded into the first computingdevice 11. The first computing device 11 thus acts as a controller 164of the three-dimensional printer 16 and controls various operations ofthe dispenser 161, servo elements 162 and the heating element 163.

In general, three-dimensional printing operations are conducted by thedispenser 161 being controlled to dispense three-dimensional printingmaterials along a substrate or an underlying layer while moving from onepoint to another. The dispensed three-dimensional printing materialhardens and thus forms a new layer on which an additional layer may bedispensed. The temperature and rate of dispensation of thethree-dimensional printing materials at the moment of dispensation ismaterial and object specific, which means that the temperature and therate of dispensation can vary based on multiple factors. The factorsinclude the size/spatial dimensions of the object and a type of thethree-dimensional printing materials.

With reference to FIGS. 3-5, it is to be understood that thethree-dimensional printing operations may be undertaken to form simplygeometric shapes or complex geometric shapes. In either case, each layerof the object being printed may be open-ended (see FIG. 3) orclosed-ended (see FIG. 4).

In the case of open-ended layers, as shown in FIG. 3, the dispenser 161begins dispensing three-dimensional printing materials at a first orstarting point S1 and ends the dispensation at a second or ending pointE1, which is different from the starting point S1. Conversely, as shownin FIG. 4, in the case of open-ended layers, the dispenser 161 beginsdispensing three-dimensional printing materials at a first or startingpoint S2 and ends the dispensation at a second or ending point E2, whichis proximate (i.e., abutting or adjacent) to the starting point S2.

For those layers that are closed-ended, with continued reference to FIG.4 and to FIG. 5, it has been seen that the three-dimensional printingmaterials dispensed at or near the starting point at the beginning ofthe layer dispensation will tend to harden in the time taken by thedispenser 161 to complete the layer dispensation and arrive at theending point E2 near the starting point S2. As such, thethree-dimensional printing materials at or around the ending pointE2/starting point S2 may have different hardening times and patternswhereby adjacent portions of the closed-ended layers may be partiallyhardened and partially molten/soft/semi-hardened. This can leads tolocalized cracks in the closed-ended layer and, in some cases, crackpropagation throughout the resulting object.

To this end, the heating element 163 (see FIGS. 2 and 4) is provided toheat certain portions of the object to be printed during thedispensation of the closed-ended layers. The heating element 163 may befixed relative to the housing 160 or movable with or relative to eitherthe housing 160 or the dispenser 161. The heating element 163 may beprovided as a single or multiple heaters and may be provided as one ormore of a laser, a heating fluid system or a radiation emitting element.In such cases, the heating element 163 may be disposed to heat theclosed-ended layers specifically, an underlying substrate/layer or anupper surface of a closed-ended layer.

In accordance with further embodiments, as shown in FIG. 5, thedispenser 161 may be controlled to dispense three-dimensional printingmaterials in order to build and assemble layers of a given printedelement 501 and, especially for cases where the printed element 501 isclosed-ended, to additionally build wall portions 502 of suitablematerial on either side of the printed element 501 (it is to beunderstood that the wall portions 502 need not be printed by thedispenser 161 and could be formed or provided by several processes).These wall portions 502 are tightly fit to the sides of the printedelement 501 and have sufficient height to protrude above any additionallayering of three-dimensional printing materials added onto theuppermost surface of the printed element 501. Thus, when suchthree-dimensional printing materials are laid down by the dispenser 161as additional layering 503 and then maintained in liquid form by theheating element 163, the wall portions 502 serve to contain thethree-dimensional printing materials in place and to prevent undesiredflows (e.g., spillage off the sides of the printed element 501).

With reference to FIG. 6, the computer program product 100 includes acomputer readable storage medium 1001 and may be installed in a memoryunit of the first computing device 11 as firmware or as lower levelexecutable program instructions. In any case, the computer programproduct 100 is provided for proactive heating-based crack preventing inthree-dimensional printing and has first-sixth program instructions601-606 embodied therewith. The first-fourth program instructions601-604 are readable and executable by the processing circuit 20 torespectively cause the processing circuit 20 to read a three-dimensionalmodel to be printed, to determine if the read three-dimensional modelhas open-ended or closed-ended layers, for each closed-ended layer, tocalculate start and end heating times and amount of heat requirement formaterials of the closed-end layers and to control a heating of theclosed-ended layers at a nozzle of the dispenser 161, an underlyingsubstrate/layer or at an upper surface of a closed-ended layer inaccordance with the calculation during a laying down of each of theclosed-ended layers. The fifth and sixth program instructions 605 and606 respectively cause the processing circuit 20 to end the heating ofeach closed-ended layer once the closed-ended layer is completely laiddown by the dispenser 161 and to disable heating during a laying down ofopen-ended layers.

In accordance with embodiments and, with reference to FIG. 7, adeployment process of the computer program product described above isprovided. The process begins at block 300 and at block 101 with adetermination of whether the first-sixth program instructions 601-606will reside on server 15 when executed. If so, then the server 15 isidentified at block 209. The first-sixth program instructions 601-606are then transferred directly to the server 15 storage via FTP or someother protocol or by copying though the use of a shared file system atblock 210 such that the first-sixth program instructions 601-606 areinstalled on the servers at block 211.

Next, a determination is made on whether the first-sixth programinstructions 601-606 are to be deployed by having users access to thefirst-sixth program instructions 601-606 on server 15 at block 102. Ifso, the server 15 addresses that will store the first-sixth programinstructions 601-606 are identified at block 103 and a determination ismade if a proxy server is to be built at block 200 for storage. A proxyserver is a server that sits between a client application, such as a Webbrowser, of first computing device 11 and server 15 and operates byintercepting all requests to the server 15 to see if it can fulfill therequests itself (see, e.g., remote web server 15 a of FIGS. 2 and 3). Ifnot, the proxy server forwards the request to server 15. The two primarybenefits of a proxy server are to improve performance and to filterrequests.

If a proxy server is required, then the proxy server is installed atblock 201 and the first-sixth program instructions 601-606 are sent viaa protocol, such as FTP, or by being copied directly from the sourcefiles to the server 15 files via file sharing at block 202. Anotherembodiment involves sending a transaction to the (one or more) server 15that contained the process software, and have the server 15 process thetransaction and then receive and copy the process software to the server15 file system. Once the process software is stored, the users may thenaccess the first-sixth program instructions 601-606 and copy to the sameto their respective client computer file systems at block 203.Alternatively, the server 15 may automatically copy the first-sixthprogram instructions 601-606 to each client and then run an installationprogram for the first-sixth program instructions 601-606 on each clientcomputer whereby the user executes the program that installs thefirst-sixth program instructions 601-606 on his client computer at block212 and then exits the process at block 108.

At block 104, a determination is made as to whether the first-sixthprogram instructions 601-606 are to be deployed by being sent to usersvia e-mail. If a result of the determination is affirmative, the set ofusers are identified together with the addresses of the user clientcomputers at block 105 and the first-sixth program instructions 601-606are sent via e-mail to each of the users' client computers. The usersthen receive the e-mail at block 205 and detach the first-sixth programinstructions 601-606 from the e-mail to a directory on their clientcomputers at block 206. The user executes the program that installs thefirst-sixth program instructions 601-606 on his client computer at block212 and then exits the process at block 108.

Lastly, a determination is made on whether the first-sixth programinstructions 601-606 will be sent directly to user directories on theirclient computers at block 106. If so, the user directories areidentified at block 107 and the process software is transferred directlyto the user's client computer directories at block 207. This can be donein several ways such as, but not limited to, sharing the file systemdirectories and then copying from the sender's file system to therecipient user's file system or, alternatively, using a transferprotocol such as File Transfer Protocol (FTP). The users access thedirectories on their client file systems in preparation for installingthe first-sixth program instructions 601-606 at block 208, execute theprogram that installs the first-sixth program instructions 601-606 atblock 212 and then exit the process at block 108.

With reference to FIG. 8, a computer-implemented method for proactiveheating-based crack preventing in three-dimensional printing isprovided. As shown in FIG. 8, the computer-implemented method includesreading a three-dimensional model to be printed at block 801,determining if the read three-dimensional model has open-ended orclosed-ended layers at block 802, for each closed-ended layer,calculating start and end heating times and amount of heat requirementfor materials of the closed-end layers at block 803 and controlling aheating of the closed-ended layers in accordance with the calculationduring a laying down of each of the closed-ended layers at block 804.The computer-implemented method further includes ending the heating ofeach closed-ended layer once the closed-ended layer is completely laiddown at block 805 and disabling heating during a laying down ofopen-ended layers at block 806.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

The present invention may be a system, a method, and/or a computerprogram product at any possible technical detail level of integration.The computer program product may include a computer readable storagemedium (or media) having computer readable program instructions thereonfor causing a processor to carry out aspects of the present invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, configuration data for integrated circuitry, oreither source code or object code written in any combination of one ormore programming languages, including an object oriented programminglanguage such as Smalltalk, C++, or the like, and procedural programminglanguages, such as the “C” programming language or similar programminglanguages. The computer readable program instructions may executeentirely on the user's computer, partly on the user's computer, as astand-alone software package, partly on the user's computer and partlyon a remote computer or entirely on the remote computer or server. Inthe latter scenario, the remote computer may be connected to the user'scomputer through any type of network, including a local area network(LAN) or a wide area network (WAN), or the connection may be made to anexternal computer (for example, through the Internet using an InternetService Provider). In some embodiments, electronic circuitry including,for example, programmable logic circuitry, field-programmable gatearrays (FPGA), or programmable logic arrays (PLA) may execute thecomputer readable program instructions by utilizing state information ofthe computer readable program instructions to personalize the electroniccircuitry, in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce acomputer-implemented process, such that the instructions which executeon the computer, other programmable apparatus, or other device implementthe functions/acts specified in the flowchart and/or block diagram blockor blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks may occur out of theorder noted in the Figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of onemore other features, integers, steps, operations, element components,and/or groups thereof.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A computer program product for proactiveheating-based crack preventing in three-dimensional printing, thecomputer program product comprising a non-transitory computer readablestorage medium having program instructions embodied therewith, theprogram instructions being readable and executable by a processingcircuit to cause the processing circuit to: read a three-dimensionalmodel to be printed; determine whether the read three-dimensional modelhas closed-ended layers, each closed-ended layer comprising a startingpoint and an end point abutting the starting point; for eachclosed-ended layer, calculate start and end heating times and an amountof heat requirement for materials of the closed-end layers; dispense thematerials of the closed-ended layers from a dispensing nozzle toaccomplish a laying down of each of the closed-ended layers while movingthe dispensing nozzle along circuits respectively corresponding to eachof the closed-ended layers from the corresponding starting point to thecorresponding end point; and control a heating of the closed-endedlayers in accordance with the calculation during the laying down of eachof the closed-ended layers, wherein the control of the heating isexecuted such that the starting point of each closed-ended layer ismaintained in a liquid state by the heating from a time at which thematerials of the closed-ended layers at the starting point are laid downuntil the materials of the closed-ended layers at the end point of thatclosed-ended layer are laid down.
 2. The computer program productaccording to claim 1, wherein the program instructions further cause theprocessing circuit to end the heating of each closed-ended layer oncethe closed-ended layer is completely laid down.
 3. The computer programproduct according to claim 1, wherein the program instructions furthercause the processing circuit to disable heating during a laying down ofopen-ended layers of the read three-dimensional model.
 4. The computerprogram product according to claim 1, wherein the program instructionsfurther cause the processing circuit to control the heating at adispensing nozzle.
 5. The computer program product according to claim 1,wherein the program instructions further cause the processing circuit tocontrol the heating at a substrate or an underlying layer.
 6. Thecomputer program product according to claim 1, wherein the programinstructions further cause the processing circuit to control the heatingat an upper surface of each closed-ended layer.
 7. The computer programproduct according to claim 1, wherein the program instructions furthercause the processing circuit to control the heating by way of a laser,heating fluid or exposure to radiation.
 8. A computing system forproactive heating-based crack preventing in three-dimensional printing,the computing system comprising a non-transitory computer readablestorage medium having instructions stored thereon that are executable bya processing circuit to cause the processing circuit to: read athree-dimensional model to be printed; determine whether the readthree-dimensional model has closed-ended layers, each closed-ended layercomprising a starting point and an end point abutting the startingpoint; for each closed-ended layer, calculate start and end heatingtimes and amount of heat requirement for materials of the closed-endlayers; dispense the materials of the closed-ended layers from adispensing nozzle to accomplish a laying down of each of theclosed-ended layers while moving the dispensing nozzle along circuitsrespectively corresponding to each of the closed-ended layers from thecorresponding starting point to the corresponding end point; and controla heating of the closed-ended layers in accordance with the calculationduring the laying down of each of the closed-ended layers, wherein thecontrol of the heating is executed such that the starting point of eachclosed-ended layer is maintained in a liquid state by the heating from atime at which the materials of the closed-ended layers at the startingpoint are laid down until the materials of the closed-ended layers atthe end point of that closed-ended layer are laid down.
 9. The computingsystem according to claim 8, wherein the instructions further cause theprocessing circuit to end the heating of each closed-ended layer oncethe closed-ended layer is completely laid down.
 10. The computing systemaccording to claim 8, wherein the instructions further cause theprocessing circuit to disable heating during a laying down of open-endedlayers of the read three-dimensional model.
 11. The computing systemaccording to claim 8, wherein the instructions further cause theprocessing circuit to control the heating at a dispensing nozzle. 12.The computing system according to claim 8, wherein the instructionsfurther cause the processing circuit to control the heating at asubstrate or an underlying layer.
 13. The computing system according toclaim 8, wherein the instructions further cause the processing circuitto control the heating at an upper surface of each closed-ended layer.14. The computing system according to claim 8, wherein the instructionsfurther cause the processing circuit to control the heating by way of alaser, heating fluid or exposure to radiation.